A new dataset-level non-strict symmetry measure allows deriving bounded equivariance for restoration models and motivates an adaptive network that aligns with per-sample symmetry to reduce expected risk.
Frame averaging for invariant and equivariant network design
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Canonization produces generalization bounds ranging from invariant-optimal to non-invariant depending on regularity, with Hilbert-curve ordering proven to give polynomial covering-number growth for point clouds while lexicographic sorting gives exponential growth.
Sublinear neural networks parametrize convex sets by learning their support and gauge functions, backed by a universal approximation theorem and tested on shape optimization tasks.
Equivariant Poincaré ResNets combine hyperbolic geometry with C4 and D4 group symmetries via specialized reshaping, permutations, and batch norm to reduce optimization space and speed convergence while staying inside the Poincaré ball.
Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
Benchmark study of ten GNN explainers on eight architectures and six datasets that isolates usable components and issues practical recommendations.
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Parametrizing Convex Sets Using Sublinear Neural Networks
Sublinear neural networks parametrize convex sets by learning their support and gauge functions, backed by a universal approximation theorem and tested on shape optimization tasks.